The Players Association filed for an arbitration hearing yesterday to fight a loophole in the new collective bargaining agreement that could give the Knicks a lot more flexibility to re-sign Jeremy Lin while preserving their $5 million mid-level exception.

That mid-level exception could be used to net a very capable point-guard counterpart — even Steve Nash — and change the landscape of the Knicks’ summer.

In what could become known as “The Linsanity Rule,’’ the union will legally challenge a bylaw in which a player claimed off waivers loses his Bird rights. Lin was claimed off waivers by the Knicks in late December from the Rockets after previously being waived by the Warriors, who owned Lin’s Bird rights. Steve Novak also was claimed off waivers.

Under the status quo, the Knicks plan to use their $5 million mid-level exception to re-sign Lin, giving them very little salary-cap room to add another solid point guard.

If the Knicks retain their $5M mid-level exception while re-signing Lin as a Bird-rights player, they would be in the market for Nash, Andre Miller, Jason Kidd, Jameer Nelson and Goran Dragic. Nash seems a reach for $5 million after leading the NBA in assists and with the Suns ready to bowl him over with a more lucrative offer.

The union will argue a player who is traded still keeps his Bird rights, so one claimed off waivers should as well.

“It’s more than ambigious,’’ union lead attorney Ron Klempner told The Post. “We believe a player claimed is no different than a player traded.’’

Novak is in a similar boat. The Knicks probably would be outbid if they offered Novak their lower exception of $2 million. The union claims there never has been a case in which a player was claimed and found himself in a situation of seeking more than the minimum in free agency. The union is fighting the battle mostly because of the Knicks’ unprecedented situation, although there are other players in a similar situation.

Interim coach Mike Woodson said Lin would return, but does not want to commit to him as the starter with eyes on adding a veteran. If they only have their $2 million exception, Raymond Felton, Derek Fisher and Gary Neal may be their best options.

Lin, meanwhile, got his wish of being named to the U.S. Select Team that will scrimmage against the U.S. Olympic Team in July in Las Vegas.